Download Objectives

Objectives
Chapter 1
Skills
A.
B.
C.
D.
E.
F.
Evaluate expressions and formulas, including correct units in answers.
Use function notation.
Solve and check linear equations.
Rewrite formulas.
Evaluate sequences.
Write a recursive definition for a sequence.
Properties
G. Determine whether a relation defined by a table, a list of ordered pairs, or a simple
equation is a function.
H. Determine the domain and range of a function defined by a table, a list of
ordered pairs, or a simple equation.
Uses
I. Use addition, subtraction, multiplication, and division to write expressions
which model real-world problems.
J. Use functions to solve real-world situations.
K. Use linear equations to solve real-world problems.
Representations
L. Determine the domain, range, and values of a function from its graph.
M. Apply the Vertical-Line Test for a function.
Chapter 2
Skills
A. Translate variation language into formulas and formulas into variation language.
B. Solve variation problems.
C. Find slopes (rates of change).
Properties
D. Use the Fundamental Theorem of Variation.
E. Identify the properties of variation functions.
Uses
F. Recognize variation situations.
G. Solve real-world variation problems.
H. Fit an appropriate model to data.
Representations
I. Graph variation equations.
J. Identify variation equations from graphs.
K. Recognize the effects of a change in scale or viewing window on a graph of a variation
equation.
Chapter 3
Skills
A.
B.
C.
D.
Determine the slope and intercepts of a line given its equation.
Find an equation for a line given two points on it or given a point on it and its slope.
Evaluate expressions based on step functions.
Evaluate or find explicit and recursive formulas for arithmetic sequences.
Properties
E. Recognize properties of linear functions.
F. Recognize properties of arithmetic sequences.
Uses
G. Model constant-increase or constant-decrease situations or situations involving
arithmetic sequences.
H. Model situations leading to linear combinations.
I. In a real-world context, find an equation for a line containing two points.
J. Fit lines to data.
K. Model situations leading to piecewise-linear functions or step functions.
Representations
L. Graph or interpret graphs of linear equations.
M. Graph or interpret graphs of piecewise-linear functions or step functions.
Chapter 4
Skills
A. Add, subtract, and find scalar multiples of matrices.
B. Multiply matrices.
C. Determine equations of lines of perpendiculars to given lines.
Properties
D. Recognize properties of matrix operations.
E. Recognize relationships between figures and their transformation images.
F. Relate transformations to matrices, and vice versa.
Uses
G. Use matrices to store data.
H. Use matrix addition, matrix multiplication, and scalar multiplication to solve real-world
problems.
Representations
I. Graph figures and their transformation images.
Chapter 5
Skills
A. Solve 2 x 2 and 3 x 3 systems using the Linear Combination Method or substitution. (53, 5-4)
B. Find the determinant and the inverse of a square matrix. (5-5)
C. Use matrices to solve systems of two or three linear equations. (5-6)
Properties
D. Recognize properties of systems of equations. (5-2, 5-3, 5-4, 5-6)
E. Recognize properties of systems of inequalities. (5-8, 5-9)
Uses
F. Use systems of two or three linear equations to solve real-world problems. (5-3, 5-4, 56)
G. Use linear programming to solve real-world problems. (5-9, 5-10)
Representations
H.
I.
J.
K.
Solve and graph linear inequalities in one variable. (5-1)
Estimate solutions to systems by graphing. (5-2)
Graph linear inequalities in two variables. (5-7)
Solve systems of inequalities by graphing. (5-1, 5-8)
Chapter 6
Skills
A.
B.
C.
D.
Expand squares of binomials.
Transform quadratic equations from vertex form to standard form, and visa versa.
Solve quadratic equations.
Perform operations with complex numbers.
Properties
E. Apply the definition of absolute value and the Absolute Value-Square Root Theorem.
F. Use the discriminant of a quadratic equation to determine the nature of the solutions to
the equation.
Uses
G. Use quadratic equations to solve area problems or problems dealing with velocity and
acceleration.
H. Fit a quadratic model to data.
I. Use the Graph-Translation Theorem to interpret equations and graphs.
Representations
J. Graph quadratic functions or absolute value functions and interpret them.
K. Use the discriminant of a quadratic equation to determine the number of x-intercepts of
the graph.
Chapter 7
Skills
A.
B.
C.
D.
Evaluate bn when b > 0 and n is a rational number.
Simplify expressions or solve equations using properties of exponents.
Describe geometric sequences explicitly and recursively.
Solve equations of the form xn = b where n is a rational number.
Properties
E. Recognize properties of the nth powers and nth roots.
Uses
F. Solve real-world problems which can be modeled by expressions with nth powers or
nth roots.
G. Apply the compound interest formula.
H. Solve real-world problems involving geometric sequences.
Representations
I. Graph nth power functions.
Chapter 8
Skills
A.
B.
C.
D.
E.
Find the values and rules for composites of functions.
Find the inverse of a relation.
Evaluate radicals.
Rewrite or simplify expressions with radicals.
Solve equations with radicals.
Properties
F. Apply properties of the inverse relations and inverse functions.
G. Apply properties of radicals and nth root functions.
Uses
H. Solve real-world problems which can be modeled by equations with radicals.
Representations
I. Make and interpret graphs of inverses of relations.
Chapter 9
Skills
A. Determine values of logarithms.
B. Use logarithms to solve exponential equations.
C. Solve logarithmic equations.
Properties
D. Recognize properties of exponential functions.
E. Identify or apply properties of logarithms.
Uses
F. Apply exponential growth and decay models.
G. Fit an exponential model to data.
H. Apply logarithmic scales (pH, decibel), models, and formulas.
Representations
I. Graph exponential functions.
J. Graph logarithmic curves.
Chapter 10
Skills
A. Approximate values of trigonometric functions using a calculator.
B. Find exact values of trigonometric functions of multiples of 30° or 45° or their radian
equivalents.
C. Determine the measure of an angle given its sine, cosine, or tangent.
D. Convert angle measures from radians to degrees or from degrees to radians.
Properties
E. Identify and use definitions and theorems relating sines, cosines, and tangents.
Uses
F. Solve real-world problems using the trigonometry of right triangles.
G. Solve real-world problems using the Law of Sines or Law of Cosines.
Representations
H. Find missing parts of a triangle using the Law of Sines or the Law of Cosines.
I. Use the properties of a unit circle to find trigonometric values.
J. Identify properties of the sine, cosine, and tangent functions using their graphs.
Chapter 11
Skills
A.
B.
C.
D.
Use the Extended Distributive Property to multiply polynomials.
Factor polynomials.
Find zeros of polynomial functions by factoring.
Determine an equation for a polynomial function from data points.
Properties
E. Use technical vocabulary to describe polynomials.
F. Apply the Zero-Product Theorem, Factor Theorem, and Fundamental Theorem of
Algebra.
G. Apply the Rational-Zero Theorem.
Uses
H. Use polynomials to model real-world situations.
I. Use polynomials to describe geometric situations.
Representations
J. Graph polynomial functions.
K. Estimate zeros of functions of polynomials using tables or graphs.
Culture
L. Be familiar with the history of the solving of polynomial equations.
Chapter 12
Skills
A. Rewrite an equation for a conic section in the general form of a quadratic equation in
two variables.
B. Write equations or inequalities for quadratic relations given sufficient conditions.
C. Find the area of an ellipse.
D. Solve systems of one linear and one quadratic equation or two quadratic equations by
substitution or linear combination.
Properties
E. Find points on a conic section using the definition of a conic.
F. Identify characteristics of parabolas, circles, ellipses, and hyperbolas.
G. Classify curves as circles, ellipses, parabolas, or hyperbolas using algebraic or
geometric properties.
Uses
H. Use circles, ellipses, and hyperbolas to solve real-world problems.
I. Use systems of quadratic equations to solve real-world problems.
J. Graph quadratic relations given sentences from them, and vice versa.
Representations
K. Solve systems of quadratic equations graphically.
Chapter 13
Skills
A.
B.
C.
D.
E.
Calculate values of a finite arithmetic series.
Calculate values of finite geometric series.
Use summation ( ) or factorial (!) notation.
Calculate permutations and combinations.
Expand binomials.
Properties
F. Recognize properties of Pascal's triangle.
Uses
G.
H.
I.
J.
Solve real-world problems using arithmetic or geometric series.
Solve problems involving permutations or combinations.
Use measures of central tendency or dispersion to describe data or distributions.
Solve problems using probability.
Representations
K. Give reasons for sampling.
L. Graph and analyze binomial and normal distributions.
Vocabulary
Lesson 1-1
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variable
algebraic expression
expression
algebraic sentence
evaluating an expression
order of operations
formula
equation
Lesson 1-2
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function
independent variable
dependent variable
is a function of
domain of a function
range of a function
input, output
natural numbers
counting numbers
whole numbers
integers
rational numbers
real numbers
Lesson 1-3
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f(x) notation
argument of a function
values of a function
arrow, or mapping, notation
Lesson 1-4
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relation
Vertical-Line Test
Lesson 1-5
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Distributive Property
"clearing" fractions
Opposite of a Sum Theorem
Lesson 1-6
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solved for a variable
in terms of
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pitch
Lesson 1-7
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sequence
term of a sequence
triangular numbers
explicit formula
subscript
subscripted variable
index
generate the terms of a sequence
Lesson 1-8
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recursive formula
recursive definition
Calculator ANS key
Lesson 1-9
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Fibonacci sequence
Lesson 2-1
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varies directly as
constant of variation
direct variation
directly proportional to
Lesson 2-2
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varies inversely as
inverse variation
inversely proportional to
fulcrum
Law of the Lever
inverse square variation
conjecture, prove
Lesson 2-3
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Fundamental Theorem of Variation
Lesson 2-4
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slope
rate of change
Lesson 2-5
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automatic grapher
window
default window
parabola
reflection symmetry
line of symmetry
copy
trace
opens up
opens down
Lesson 2-6
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hyperbola
branches of a hyperbola
discrete
inverse-square curve
vertical asymptote
horizontal asymptote
Lesson 2-7
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mathematical model
Lesson 2-8
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Converse of the Fundamental Theorem of Variation
Lesson 2-9
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combined variation
joint variation
Lesson 3-1
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y-intercept
initial condition
slope-intercept
linear function
constant-increase situation
constant-decrease situation
slope
piecewise-linear graph
Lesson 3-3
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linear-combination situation
Lesson 3-4
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standard form
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x-intercept
vertical line
oblique line
horizontal line
Lesson 3-5
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scatterplot
regression line
line of best fit
least squares line
correlation coefficient
Lesson 3-7
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constant difference
arithmetic sequence
linear sequence
recursive formula for an arithmetic sequence
Lesson 3-8
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explicit formula for an arithmetic sequence
Lesson 3-9
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step function
greatest-integer function
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rounding-down function
floor function
INT (x)
Vocabulary
Lesson 4-1
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matrix, matrices
element of a matrix
dimensions n m
row
column
equal matrices
point matrix
Lesson 4-2
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matrix addition
sum of matrices
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difference of matrices
scalar multiplication
Lesson 4-3
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matrix multiplication
headings
2 2 identity matrix
Lesson 4-4
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standard form
transformation
size change, S
preimage
image
similar
ratio of similitude
center
magnitude of size change
identity transformation
Lesson 4-5
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scale change, Sa,b
horizontal magnitude
vertical magnitude
stretch, shrink
Lesson 4-6
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reflection image of a point over a line
reflection image
reflecting line
line of reflection
reflection
rx , ry , rx = y
Matrix Basis Theorem
Lesson 4-7
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closure
composite of transformation
composed
R90
Lesson 4-8
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rotation
Rx, R90, R180, R270,
Lesson 4-10
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translation, Th,k
slide or translation image
Vocabulary
Lesson 5-1
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constraint
system
open sentence
interval
compound sentence
*union of sets, or
*intersection of sets, and
inequality
Addition Property of Inequality
Multiplication Properties of Inequality
Lesson 5-2
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system
*solution for a system
rescale, zoom
Lesson 5-3
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consistent system
inconsistent system
Lesson 5-4
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Linear Combination Method
Lesson 5-5
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*Inverse of a matrix M, M–1
Square matrix
Inverse Matrix Theorem
*determinant of a 2 x 2 matrix M
det M
Lesson 5-6
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matrix form of a system
coefficient matrix
constant matrix
System-Determinant Theorem
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3 x 3 identity matrix
Lesson 5-7
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half-plane
boundary
lattice point
Lesson 5-8
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*feasible set, feasible region
*vertices of feasible region
convex region
Lesson 5-9
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linear-programming problem
Linear-Programming Theorem
Vocabulary
Lesson 6-1
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quadratic
quadratic expression
quadratic function
standard form of a quadratic
Binomial Square Theorem
Lesson 6-2
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absolute value
absolute value function
Absolute Value-Square Root Theorem
square root
simple fraction
irrational number
Lesson 6-3
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*Graph-Translation Theorem
corollary
vertex form of an equation of a parabola
axis of symmetry
minimum, maximum
Lesson 6-4
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standard form of an equation of a parabola
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acceleration due to gravity
h = gt2 + v0t + h0
velocity
Lesson 6-5
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completing the square
perfect-square trinomial
Lesson 6-6
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quadratic model
quadratic regression
Lesson 6-7
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*Quadratic Formula
standard form of a quadratic equation
Lesson 6-8
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*
* ,i
imaginary number
Lesson 6-9
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*complex number
*real part, imaginary part
*equal complex numbers
impedance
circuit in series, in parallel
*complex conjugate
hierarchy
Lesson 6-10
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*discriminant of a quadratic equation
nature of the solutions
*root of an equation
Discriminant Theorem
Vocabulary
Lesson 7-1
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powering
exponentiation
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base
exponent
power repeated multiplication
nth power function
identity function
2nd power
squaring function
cubing function
Lesson 7-2
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Product of Powers Postulate
Power of a Power Postulate
Power of a Product Postulate
Quotient of Powers Postulate
Power of a Quotient Postulate
Zero Exponent Theorem
Lesson 7-3
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Negative Exponent Theorem
Lesson 7-4
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compounded annually
compounded semiannually
compounded quarterly
principal
Compound Interest Formula
General Compound Interest Formula
effective annual yield
yield
simple interest
Lesson 7-5
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geometric sequence
exponential sequence
constant multiplier
constant ratio
recursive formula for a geometric sequence
explicit formula for a geometric sequence
Lesson 7-6
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square root
cube root
nth root
Exponent Theorem
Number of Real Roots Theorem
Lesson 7-7
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Rational Exponent Theorem
Vocabulary
Lesson 8-1
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radical notation
composite of s and f, s f
function composition
Lesson 8-2
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inverse of a relation
Horizontal Line Test for Inverses
Lesson 8-3
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Inverse Functions Theorem
f–1
identity function
Lesson 8-4
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radical sign, radical
when x 0
Root of a Power Theorem
Lesson 8-5
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Root of a Product Theorem
simplified form
simplify an nth root
geometric mean
Lesson 8-6
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rationalizing the denominator
conjugate
Lesson 8-7
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when x < 0
Lesson 8-8
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Vocabulary
extraneous roots
Lesson 9-1
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exponential function
exponential curve
exponential growth
Lesson 9-2
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exponential decay
depreciation
half-life
Exponential Growth Model
Lesson 9-3
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continuous compounding
instantaneous compounding
e
Continuously Compounding Interest Formula
Continuous Change Model
Lesson 9-4
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decade growth factor
yearly (annual) growth factor
Lesson 9-5
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logarithm of x with base 10, log x
logarithmic curve
*common logarithm
common logarithm function
logarithmic equations
Lesson 9-6
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logarithmic scale
Richter scale
bel, decibel
pH
base, acid
acidic
alkaline
linear scale
Lesson 9-7
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*Logarithm of m with base b, logb m
Lesson 9-8
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Logarithm of 1 Property
logb of bn Property
Product Property of Logarithms
Quotient Property of Logarithms
Power Property of Logarithms
Lesson 9-9
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*natural logarithm of x, ln x
Lesson 9-10
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Change of Base Property
Vocabulary
Lesson 10-1
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trigonometry
trigonometric ratios
*sine of , sin ,
*cosine of , cos ,
*tangent of , tangent ,
bearing
Lesson 10-2
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inverse trigonometric functions, sin–1, cos–1, tan–1
angle of elevation
line of sight
angle of depression
Lesson 10-3
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Complements Theorem
Pythagorean Identity
Tangent Theorem
Exact-Value Theorem
Lesson 10-4
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Unit Circle
Lesson 10-5
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signs of sine and cosine in quadrants II-IV
Lesson 10-6
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Law of Cosines
Lesson 10-7
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Law of Sines
triangulation
refracted
Snell's Law
Lesson 10-8
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*cosine function
*sine function
periodic function, period
sine wave
sinusoidal
Lesson 10-10
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radian, rad
Conversion Factors for Degrees and Radians
Vocabulary
Lesson 11-1
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*polynomial in x
*degree of a polynomial term
*standard form of a polynomial
*coefficients of a polynomial
leading coefficient
expanding a polynomial
*linear, quadratic, cubic, quartic
polynomials
polynomial equation, polynomial function
symbol manipulator
Lesson 11-2
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monomial
binomial
trinomial
degree of a polynomial in several variables
Extended Distributive Property
Lesson 11-3
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factored form
factoring
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Binomial Square Factoring Theorem
Difference-of-Squares Factoring Theorem
Discriminant Theorem for Factoring Quadratics
prime polynomial, irreducible polynomial
Lesson 11-4
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key
Lesson 11-5
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Zero-Product Theorem
*zero of a function
factor
Factor Theorem
Lesson 11-7
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Rational-Zero Theorem
Lesson 11-8
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quartic, quintic equations
Fundamental Theorem of Algebra
double root, multiplicity of a root
Number of Roots of a Polynomial Equation Theorem
Lesson 11-9
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Polynomial-Difference Theorem
Vocabulary
Lesson 12-1
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*quadratic equation in two variables
*quadratic relation in two variables
double cone
conic section, conic
*parabola
focus, directrix
axis of symmetry
vertex
paraboloid
Lesson 12-2
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*circle, radius, center
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concentric circles
*Center-Radius Equation for a Circle Theorem
Lesson 12-3
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*interior, exterior, of a circle
*boundary
*Interior and Exterior of a Circle Theorem
Lesson 12-4
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conic graph paper
*ellipse
foci, focal constant
standard position for an ellipse
Equation for an Ellipse Theorem
standard form of equation for an ellipse
*major axis, minor axis, center of an ellipse
vertex, vertices of an ellipse
Lesson 12-5
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Graph Scale-Change Theorem
area of an ellipse
eccentricity of an ellipse
Lesson 12-6
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*hyperbola
foci, focal constant
vertices of a hyperbola
asymptotes of a hyperbola
Equation for a Hyperbola Theorem
*standard form for an equation of a hyperbola
Lesson 12-7
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*rectangular hyperbola
*standard form for a quadratic relation
Lesson 12-8
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quadratic system
quadratic-linear system
Lesson 12-9
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quadratic-quadratic system
Vocabulary
Lesson 13-1
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*series
*arithmetic series
Lesson 13-2
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*geometric series
Lesson 13-3
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, sigma
-notation, sigma notation, summation notation
index variable, index
!, factorial symbol
permutation
Lesson 13-4
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*mean
*median
*mode
statistical measure
measure of center or of central tendency
standard deviation
Lesson 13-5
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Pascal's triangle
Pascal's Triangle Explicit Formula Theorem
Lesson 13-6
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binomial expansion
Binomial Theorem
binomial coefficients
Lesson 13-7
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subset
*combination
Lesson 13-8
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*independent events
*mutually exclusive events
binomial experiment
trial
Binomial Probability Theorem
Lesson 13-9
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lottery
Lesson 13-10
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probability function
probability distribution
binomial distribution, binomial probability distribution
normal distribution
normal curve
standardized scores, normalized scores
Lesson 13-11
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*population
*sample
random sample
stratified sample
random numbers
Central Limit Theorem